Question

date: ____ per. ____

directions: write each polynomial in standard form.

1. $-14 + 9x$ \t\t2. $7w^3 + 25 - 2w$ \t\t3. $-1 - 4a^2 + 17a$
2. $3p + 2p^2 - 16p^3$ \t\t5. $-6 + 8m^2 - 4m + 9m^3$ \t\t6. $k - 17 - 2k^3 + 14k^2$

directions: find each sum/difference. write all answers in standard form.

1. $(3a + 6) + (6a + 7)$ \t\t8. $(4n - 6) - (3n + 2)$
2. $(4x + 7) - (8 - 3x)$ \t\t10. $(9c - 2) + (1 - c)$
3. $(x^2 + 7x - 6) + (x^2 + 6x + 3)$ \t\t12. $(v^2 + 7v - 5) - (6v^2 + 4v - 5)$
4. $(4c^2 - 8c + 1) + (1 - 8c - 2c^2)$ \t\t14. $(4k^2 - 5 - 4k) - (9k - 2 - 5k^2)$
5. $(7m^2 - 3 + m) - (2m + 3 + 10m^2)$ \t\t16. $(r^2 - r + 1) + (-3 + 2r + 6r^2)$
6. find the sum of $3 - a - 5a^2$ and $a - 7a^2 - 3$. \t\t18. find the difference of $5k^2 - 7k + 6$ and $3k - 4k^2 + 1$.
7. subtract $8x - 3x^3 + 6$ from $7 - 6x + 5x^3$. \t\t20. what is $8x + 11$ less than the product of $-2$ and $x - 7$?

Explanation:

Let's solve problem 7: \((3a + 6) + (6a + 7)\)

Step 1: Remove the parentheses

Since there are no negative signs outside the parentheses, we can directly remove them: \(3a + 6 + 6a + 7\)

Step 2: Combine like terms

Combine the \(a\)-terms: \(3a+6a = 9a\)
Combine the constant terms: \(6 + 7 = 13\)

Step 3: Write the result

Put the combined terms together: \(9a + 13\)

Answer:

\(9a + 13\)